public YieldTermStructure fitSwap(int curveIndex, BasicFixedLeg swap, YieldTermStructure curve, double swapRate)
{
int nPayments = swap._nPayments;
int nNodes = curve.nJumps_;
double t1 = curveIndex == 0 ? 0.0 : curve.t[curveIndex - 1];
double t2 = curveIndex == nNodes - 1 ? double.PositiveInfinity : curve.t[curveIndex + 1];
double temp = 0;
double temp2 = 0;
int i1 = 0;
int i2 = nPayments;
double[] paymentAmounts = new double[nPayments];
for (int i = 0; i < nPayments; i++)
{
double t = swap.getPaymentTime(i);
paymentAmounts[i] = swap.getPaymentAmounts(i, swapRate);
if (t <= t1)
{
double df = Math.Exp(-curve.getRT_(t));
temp += paymentAmounts[i] * df;
temp2 -= paymentAmounts[i] * curve.getSingleNodeDiscountFactorSensitivity(t, curveIndex);
i1++;
}
else if (t >= t2)
{
double df = Math.Exp(-curve.getRT_(t));
temp += paymentAmounts[i] * df;
temp2 += paymentAmounts[i] * curve.getSingleNodeDiscountFactorSensitivity(t, curveIndex);
i2--;
}
}
double cachedValues = temp;
double cachedSense = temp2;
int index1 = i1;
int index2 = i2;
BracketRoot BRACKETER = new BracketRoot();
NewtonRaphsonSingleRootFinder ROOTFINDER = new NewtonRaphsonSingleRootFinder();
Func <double, double> func = x => apply_(x, curve, curveIndex, cachedValues, index1, index2,
swap, paymentAmounts);
Func <double, double> grad = x => apply_sen(x, curve, curveIndex, cachedSense, index1, index2,
swap, swapRate);
double guess = curve.getZeroRateAtIndex(curveIndex);
if (guess == 0.0 && func(guess) == 0.0)
{
return(curve);
}
double[] bracket = BRACKETER.getBracketedPoints(func, 0.8 * guess, 1.25 * guess, 0, double.PositiveInfinity);
double r = ROOTFINDER.getRoot(func, grad, bracket[0], bracket[1]);
return(curve.withRate(r, curveIndex));
}
public double ProtectionLegNPV_Exact(CDS cds, double notional, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double recoveryrate, List <double> Jumps, List <double> creditCurveKnot)
{
DateTime Stepindate = tradedate.AddDays(1);
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
double t0 = 0;
double T = cds.getProtectionEnd();
List <double> JumpNodes = new List <double>();
JumpNodes.Add(t0);
for (int j = 0; j < Jumps.Count; j++)
{
if (Jumps[j] < T)
{
JumpNodes.Add(Jumps[j]);
}
}
JumpNodes.Add(T);
double ht0 = hazard.getRT_(JumpNodes[0]);
double rt0 = yt.getRT_(JumpNodes[0]);
double b0 = Math.Exp(-ht0 - rt0); // risky discount factor
double pv = 0.0;
double dPV = 0.0;
for (int i = 1; i < JumpNodes.Count; ++i)
{
double ht1 = hazard.getRT_(JumpNodes[i]);
double rt1 = yt.getRT_(JumpNodes[i]);
double b1 = Math.Exp(-ht1 - rt1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
// The formula has been modified from ISDA (but is equivalent) to avoid log(exp(x)) and explicitly
// calculating the time step - it also handles the limit
if (Math.Abs(dhrt) < 1e-5)
{
dPV = dht * b0 * (Math.Exp(-dhrt) - 1) / (-dhrt);
}
else
{
dPV = (b0 - b1) * dht / dhrt;
}
pv += dPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
return(pv * notional * (1 - recoveryrate) / yt.discount(settlementDate));
}
public double PremiumLegNPV_Exact(CDS cds, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double notional, double coupon, List <double> Jumps, DateTime lastpayment)
{
double ita = (double)365 / 360;
double totalNPV = 0.0;
CdsCoupon[] cf = cds.getCoupons();
for (int i = 0; i < cf.Length; ++i)
{
totalNPV += cf[i].getYearFrac() * notional * Math.Exp(-hazard.getRT_(cf[i].getEffEnd()))
* Math.Exp(-yt.getRT_(cf[i].getEffEnd()));
}
double accrualpaidondefault = calculateSinglePeriodAccrualOnDefault(cf, coupon, tradedate, yt, hazard, lastpayment);
totalNPV += ita * coupon * accrualpaidondefault * notional / yt.discount(tradedate.AddDays(3));
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
Calendar calendar = new UnitedStates();
return(totalNPV / Math.Exp(-yt.getRT_(cds.getCashSettleTime())));
}
public double apply_(double x, YieldTermStructure curve, int curveIndex, double cachedValues, int index1, int index2,
BasicFixedLeg swap, double[] paymentAmounts)
{
YieldTermStructure tempCurve = curve.withRate(x, curveIndex);
double sum = 1.0 - cachedValues; // Floating leg at par
for (int i = index1; i < index2; i++)
{
double t = swap.getPaymentTime(i);
sum -= paymentAmounts[i] * Math.Exp(-tempCurve.getRT_(t));
}
return(sum);
}
/**
* The intrinsic annuity of a CDS portfolio (index) for a unit (initial) notional.
* The value of the premium leg is this multiplied by the <b> initial</b> notional of the index
* and the index coupon (as a fraction).
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param priceType Clean or dirty
* @param valuationTime Valuation time. The leg value is calculated for today (t=0),
* then rolled forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The intrinsic annuity of a CDS portfolio (index)
*/
public double indexAnnuity(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
CdsPriceType priceType,
double valuationTime)
{
int n = intrinsicData.getIndexSize();
double a = 0;
for (int i = 0; i < n; i++)
{
if (!intrinsicData.isDefaulted(i))
{
a += intrinsicData.getWeight(i) * _pricer.annuity(indexCDS, yieldCurve, intrinsicData.getCreditCurve(i), priceType, 0);
}
}
a /= Math.Exp(-yieldCurve.getRT_(valuationTime));
return(a);
}
/**
* The normalised intrinsic value of the protection leg of a CDS portfolio (index).
* The actual value of the leg is this multiplied by the <b>initial</b> notional of the index.
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param valuationTime Valuation time. The leg value is calculated for today (t=0),
* then rolled forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The normalised intrinsic value of the protection leg.
*/
public double indexProtLeg(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
double valuationTime)
{
CDS cds = indexCDS.withRecoveryRate(0.0);
int n = intrinsicData.getIndexSize();
double protLeg = 0;
for (int i = 0; i < n; i++)
{
if (!intrinsicData.isDefaulted(i))
{
protLeg += intrinsicData.getWeight(i) * intrinsicData.getLGD(i) *
_pricer.protectionLeg(cds, yieldCurve, intrinsicData.getCreditCurve(i), 0);
}
}
protLeg /= Math.Exp(-yieldCurve.getRT_(valuationTime));
return(protLeg);
}
public double calculateSinglePeriodAccrualOnDefault(CdsCoupon[] cf, double coupon,
DateTime tradedate,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve, DateTime lastpayment)
{
double Acc = 0;
DateTime effectiveStart = tradedate.AddDays(1);
for (int i = 0; i < cf.Length; ++i)
{
//Accured on default
double t_0 = (i > 0) ? cf[i].getEffStart() : 0;
double T = cf[i].getEffEnd();
T = cf[i].getPaymentTime();
List <double> knots = new List <double>();
knots.Add(t_0);
for (int j = 0; j < yieldCurve.t.Count; j++)
{
if ((yieldCurve.t[j] < T) && (t_0 < yieldCurve.t[j]))
{
knots.Add(yieldCurve.t[j]);
}
}
knots.Add(T);
double t = knots[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double b0 = Math.Exp(-rt0 - ht0); // this is the risky discount factor
OMLib.Conventions.DayCount.Actual365 dc = new OMLib.Conventions.DayCount.Actual365();
double t0;
if (i == 0)
{
t0 = knots[0] - cf[0].getEffStart();
}
else
{
t0 = knots[0] - cf[i].getEffStart();
}
double pv = 0.0;
int nItems = knots.Count;
for (int j = 1; j < nItems; ++j)
{
t = knots[j];
double ht1 = creditCurve.getRT_(t);
double rt1 = yieldCurve.getRT_(t);
double b1 = Math.Exp(-rt1 - ht1);
double dt = knots[j] - knots[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt + 1e-50;
double tPV;
double t1;
if (i == 0)
{
t1 = knots[j] - cf[0].getEffStart();
}
else
{
t1 = knots[j] - cf[i].getEffStart();
}
if (Math.Abs(dhrt) < 1e-5)
{
tPV = dht * b0 * (t0 * (Math.Exp(-dhrt) - 1) / (-dhrt) + dt * ((-dhrt - 1) * (Math.Exp(-dhrt) - 1) - dhrt) / (dhrt * dhrt));
}
else
{
tPV = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
}
t0 = t1;
pv += tPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
Acc += pv;
}
return(Acc);
}